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Fractional Calculus and Applied Analysis

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Fractional variation of Hölderian functions

Dimiter Prodanov
  • Department of Environment, Health and Safety Neuroscience Research Flanders IMEC vzw, Kapeldreef 75 3001 Leuven, BELGIUM
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Published Online: 2015-05-23 | DOI: https://doi.org/10.1515/fca-2015-0036

Abstract

The paper demonstrates the basic properties of the local fractional variation operators (termed fractal variation operators). The action of the operators is demonstrated for local characterization of Hölderian functions. In particular, it is established that a class of such functions exhibits singular behavior under the action of fractal variation operators in infinitesimal limit. The link between the limit of the fractal variation of a function and its derivative is demonstrated. The paper presents a number of examples, including the calculation of the fractional variation of Cauchy sequences leading to the Dirac’s delta-function.

Keywords : fractional calculus; non-differentiable functions; singular functions; Hölder classes; pseudodifferential operators

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About the article

Received: 2014-06-20

Accepted: 2014-12-20

Published Online: 2015-05-23

Published in Print: 2015-06-01


Citation Information: Fractional Calculus and Applied Analysis, ISSN (Online) 1314-2224, ISSN (Print) 1311-0454, DOI: https://doi.org/10.1515/fca-2015-0036.

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